Background

This analysis document compliments FIA NLS Models: Biomass Growth vs. Biomass. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different growth estimators.

Here, we fit the models using: 1) calculated plot biomass growth (Mass-Balance method) using only trees >5 inches (12.5 cm) dbh (\(G_{MassBal > 5}\)), and 2) plot biomass growth (tree incremental growth method \(G_{TI}\) for trees >5 inches (12.5 cm) dbh (\(G_{TI-NoIngrow}\)).

Below the model fitting procedure is implemented by ecoprovince:

Analysis 1: \(G_{MassBal > 5}\)

211 - Northeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6822     6268.0                                
## 2   6821     6235.4  1 32.546  35.603 2.541e-09 ***
## 3   6820     6221.2  1 14.190  15.556 8.089e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 26129.23
## 2     2 26095.70
## 3     3 26082.15
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.674498   0.213888   3.154  0.00162 ** 
## phi    0.030293   0.005334   5.679 1.41e-08 ***
## alpha  0.151999   0.037929   4.007 6.20e-05 ***
## A      3.628538   0.145390  24.957  < 2e-16 ***
## k     32.613102   1.763621  18.492  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9551 on 6820 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 7.405e-06
##   (52 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6820     6221.2                                 
## 2   6819     6220.4  1  0.8511   0.933    0.3341    
## 3   6819     6219.5  0  0.0000                      
## 4   6818     6203.8  1 15.6642  17.215 3.379e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 26082.15
## 2    3a 26083.22
## 3    3b 26082.26
## 4    3c 26067.05
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.685520   0.214374   3.198  0.00139 ** 
## phi    0.029555   0.005308   5.568 2.67e-08 ***
## alpha  0.156989   0.037739   4.160 3.22e-05 ***
## A      3.224703   0.139363  23.139  < 2e-16 ***
## k     35.506210   1.992110  17.823  < 2e-16 ***
## p      0.149324   0.028956   5.157 2.58e-07 ***
## s      1.600234   0.150406  10.639  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9539 on 6818 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.559e-06
##   (52 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 17 rows containing missing values (geom_point).
## Warning: Removed 1038 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18911      19584                                 
## 2  18906      19502  5  82.115  15.921 1.097e-15 ***
## 3  18905      19391  1 111.145 108.359 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 67445.37
## 2     2 67356.53
## 3     3 67250.45
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.84684    0.16123   5.252 1.52e-07 ***
## phi    0.02882    0.00323   8.922  < 2e-16 ***
## alpha  0.27444    0.02555  10.740  < 2e-16 ***
## A      3.45910    0.10186  33.960  < 2e-16 ***
## k     44.00640    1.49322  29.471  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.013 on 18905 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.694e-06
##   (3805 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18905      19391                                 
## 2  18904      19390  1  1.6977  1.6552    0.1983    
## 3  18904      19345  0  0.0000                      
## 4  18903      19316  1 29.2713 28.6456 8.792e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 67250.45
## 2    3a 67250.80
## 3    3b 67207.54
## 4    3c 67180.91
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.891108   0.162995   5.467 4.63e-08 ***
## phi    0.028604   0.003225   8.870  < 2e-16 ***
## alpha  0.282794   0.025317  11.170  < 2e-16 ***
## A      2.795505   0.087189  32.063  < 2e-16 ***
## k     31.258390   0.943478  33.131  < 2e-16 ***
## p      0.039140   0.006911   5.664 1.50e-08 ***
## s      1.530595   0.063957  23.932  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.011 on 18903 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.168e-06
##   (3805 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1926 rows containing missing values (geom_point).
## Warning: Removed 1031 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7266     9818.9                                 
## 2   7265     9793.4  1  25.495  18.913 1.387e-05 ***
## 3   7264     9590.4  1 202.974 153.737 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 32046.10
## 2     2 32029.20
## 3     3 31878.96
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.988817   0.118035  -8.377  < 2e-16 ***
## phi    0.020771   0.005299   3.920 8.94e-05 ***
## alpha  0.519246   0.039968  12.991  < 2e-16 ***
## A      5.980923   0.201695  29.653  < 2e-16 ***
## k     32.683181   2.580097  12.667  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.149 on 7264 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.775e-06
##   (64 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7264     9590.4                                 
## 2   7263     9574.4  1 15.9945 12.1332 0.0004982 ***
## 3   7263     9559.1  0  0.0000                      
## 4   7262     9558.3  1  0.8246  0.6265 0.4286597    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 31878.96
## 2    3a 31868.83
## 3    3b 31857.20
## 4    3c 31858.57
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.027007   0.115837  -8.866  < 2e-16 ***
## phi     0.021251   0.005293   4.015 6.01e-05 ***
## alpha   0.520095   0.039723  13.093  < 2e-16 ***
## A       9.403659   1.801768   5.219 1.85e-07 ***
## k     124.281123  88.581937   1.403    0.161    
## s       0.536568   0.081920   6.550 6.15e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.147 on 7263 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 1.076e-06
##   (64 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 32 rows containing missing values (geom_point).
## Warning: Removed 1036 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4839     5394.3                                
## 2   4838     5383.2  1 11.103  9.9789  0.001593 ** 
## 3   4837     5304.5  1 78.754 71.8138 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19469.00
## 2     2 19461.02
## 3     3 19391.66
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.264563   0.215167  -1.230  0.21892    
## phi    0.025578   0.008968   2.852  0.00436 ** 
## alpha  0.425194   0.047791   8.897  < 2e-16 ***
## A      5.159553   0.234255  22.025  < 2e-16 ***
## k     40.596780   2.741230  14.810  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.047 on 4837 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.398e-06
##   (1003 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   4837     5304.5                                 
## 2   4836     5278.0  1 26.4489 24.2339 8.815e-07 ***
## 3   4836     5266.0  0  0.0000                      
## 4   4835     5266.0  1  0.0125  0.0115    0.9148    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 19391.66
## 2    3a 19369.46
## 3    3b 19358.43
## 4    3c 19360.41
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.29333    0.21184  -1.385  0.16621    
## phi     0.02365    0.00888   2.663  0.00777 ** 
## alpha   0.42418    0.04749   8.932  < 2e-16 ***
## A       9.03847    1.70448   5.303 1.19e-07 ***
## k     194.36309  112.01286   1.735  0.08277 .  
## s       0.60311    0.05671  10.636  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.044 on 4836 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 1.19e-06
##   (1003 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 489 rows containing missing values (geom_point).
## Warning: Removed 1053 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   8742      10361                               
## 2   8741      10357  1   3.59   3.0301 0.08177 .  
## 3   8740      10213  1 143.84 123.0907 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35815.03
## 2     2 35814.00
## 3     3 35693.70
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.721669   0.124982  -5.774    8e-09 ***
## phi   -0.011373   0.006206  -1.833   0.0669 .  
## alpha  0.474022   0.040713  11.643   <2e-16 ***
## A      6.220919   0.229416  27.116   <2e-16 ***
## k     61.999434   4.180720  14.830   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 8740 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 6.274e-06
##   (1265 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model     AIC
## 1     3 35693.7
## 2    3a      NA
## 3    3b      NA
## 4    3c      NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.721669   0.124982  -5.774    8e-09 ***
## phi   -0.011373   0.006206  -1.833   0.0669 .  
## alpha  0.474022   0.040713  11.643   <2e-16 ***
## A      6.220919   0.229416  27.116   <2e-16 ***
## k     61.999434   4.180720  14.830   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.081 on 8740 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 6.274e-06
##   (1265 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 620 rows containing missing values (geom_point).
## Warning: Removed 1002 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  13233      28484                                  
## 2  13232      28462  1   21.16   9.8378  0.001713 ** 
## 3  13231      27201  1 1261.55 613.6444 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66709.26
## 2     2 66701.43
## 3     3 66103.36
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.894296   0.216964   8.731   <2e-16 ***
## phi    0.011411   0.004537   2.515   0.0119 *  
## alpha  0.577267   0.021646  26.668   <2e-16 ***
## A      4.139687   0.136350  30.361   <2e-16 ***
## k     12.872682   0.733389  17.552   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.434 on 13231 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.119e-06
##   (281 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13231      27201                                
## 2  13230      27143  1 57.897  28.220 1.100e-07 ***
## 3  13230      27185  0  0.000                      
## 4  13229      27117  1 68.434  33.386 7.727e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 66103.36
## 2    3a 66077.16
## 3    3b 66097.71
## 4    3c 66066.35
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.916982   0.218104   8.789   <2e-16 ***
## phi    0.011568   0.004527   2.556   0.0106 *  
## alpha  0.578073   0.021534  26.845   <2e-16 ***
## A      3.920044   0.137509  28.508   <2e-16 ***
## k     19.579507   1.297481  15.090   <2e-16 ***
## s      1.532558   0.143087  10.711   <2e-16 ***
## p      0.215128   0.025467   8.447   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.432 on 13229 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.348e-06
##   (281 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 143 rows containing missing values (geom_point).
## Warning: Removed 1017 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1  13303      32383                                
## 2  13302      32374  1    9.09   3.7347 0.05331 .  
## 3  13301      31086  1 1287.82 551.0239 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 67119.92
## 2     2 67118.18
## 3     3 66580.06
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.217120   0.202369   6.014 1.85e-09 ***
## phi    0.004865   0.004835   1.006    0.314    
## alpha  0.552376   0.021669  25.491  < 2e-16 ***
## A      4.614507   0.160978  28.665  < 2e-16 ***
## k     19.539797   0.996769  19.603  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.529 on 13301 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.622e-06
##   (323 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13301      31086                                
## 2  13300      30996  1 89.920  38.583 5.403e-10 ***
## 3  13300      31051  0  0.000                      
## 4  13299      30980  1 71.267  30.594 3.241e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 66580.06
## 2    3a 66543.52
## 3    3b 66566.91
## 4    3c 66538.34
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.210556   0.201415   6.010 1.90e-09 ***
## phi    0.004612   0.004819   0.957    0.339    
## alpha  0.552631   0.021585  25.602  < 2e-16 ***
## A      4.470390   0.177685  25.159  < 2e-16 ***
## k     26.555408   1.622920  16.363  < 2e-16 ***
## s      1.292768   0.110039  11.748  < 2e-16 ***
## p      0.151857   0.021081   7.203 6.19e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.526 on 13299 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.492e-06
##   (323 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 169 rows containing missing values (geom_point).
## Warning: Removed 931 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1324     3585.5                                 
## 2   1323     3583.4  1   2.091  0.7719    0.3798    
## 3   1322     3425.7  1 157.702 60.8576 1.238e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6935.007
## 2     2 6936.233
## 3     3 6878.510
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.36910    1.48584   1.594    0.111    
## phi   -0.02860    0.02171  -1.318    0.188    
## alpha  0.72235    0.08409   8.590  < 2e-16 ***
## A      3.57099    0.73913   4.831 1.51e-06 ***
## k     12.61195    2.97891   4.234 2.46e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.61 on 1322 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.505e-06
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   1322     3425.7                            
## 2   1321     3417.1  1 8.6281  3.3355 0.06803 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6878.510
## 2    3a 6877.163
## 3    3b 6874.539
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.33814    1.46855   1.592  0.11159    
## phi   -0.02864    0.02168  -1.321  0.18665    
## alpha  0.71638    0.08409   8.519  < 2e-16 ***
## A      5.32758    2.10630   2.529  0.01154 *  
## k     46.97352   76.64657   0.613  0.54008    
## s      0.44452    0.16075   2.765  0.00577 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.607 on 1321 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.471e-06
##   (61 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91212, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5322, p-value = 5.837e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).
## Warning: Removed 645 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1     77     134.46                            
## 2     76     133.72  1 0.7389  0.4200 0.51890  
## 3     75     124.41  1 9.3087  5.6118 0.02041 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 422.9552
## 2     2 424.5143
## 3     3 420.7417
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge    -0.75949    2.02917  -0.374   0.7092  
## phi    0.06449    0.07007   0.920   0.3604  
## alpha  0.91258    0.34680   2.631   0.0103 *
## A      9.93416    5.09806   1.949   0.0551 .
## k     31.51695   16.45984   1.915   0.0593 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.288 on 75 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.48e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1     75     124.41                          
## 2     74     121.35  1 3.05607  1.8636 0.1763
## 3     74     121.37  0 0.00000               
## 4     73     121.21  1 0.15651  0.0943 0.7597
##   model      AIC
## 1     3 420.7417
## 2    3a 420.7519
## 3    3b 420.7622
## 4    3c 422.6590
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge    -0.75949    2.02917  -0.374   0.7092  
## phi    0.06449    0.07007   0.920   0.3604  
## alpha  0.91258    0.34680   2.631   0.0103 *
## A      9.93416    5.09806   1.949   0.0551 .
## k     31.51695   16.45984   1.915   0.0593 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.288 on 75 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.48e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8973, p-value = 9.381e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.2134, p-value = 0.225
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 725 row(s) containing missing values (geom_path).

plotting 2

251 - Prairie Parkland (Temperate)

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1785     2660.0                          
## 2   1784     2656.9  1 3.11481  2.0915 0.1483
## 3   1783     2655.9  1 0.94967  0.6375 0.4247
##   model      AIC
## 1     1 7632.934
## 2     2 7632.839
## 3     3 7634.199
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.12968    0.48733   0.266    0.790    
## phi  0.01977    0.01380   1.433    0.152    
## A    3.62465    0.35660  10.164  < 2e-16 ***
## k   24.44082    4.31621   5.663 1.73e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.22 on 1784 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.584e-06
##   (507 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", "_MBg5", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
##   model      AIC
## 1     2 7632.839
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.12968    0.48733   0.266    0.790    
## phi  0.01977    0.01380   1.433    0.152    
## A    3.62465    0.35660  10.164  < 2e-16 ***
## k   24.44082    4.31621   5.663 1.73e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.22 on 1784 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.584e-06
##   (507 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.69784, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.7342, p-value = 1.041e-14
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 254 rows containing missing values (geom_point).
## Warning: Removed 1176 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

Model selection 1

## Error in nls(fg_1_MBg5, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_MBg5, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3_MBg5, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    212     98.175                             
## 2    211     97.256  1 0.91939  1.9947 0.15933  
## 3    210     94.284  1 2.97201  6.6196 0.01078 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 485.5008
## 2     2 485.4779
## 3     3 480.8052
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge     -1.42305    0.79743  -1.785  0.07578 . 
## phi    -0.07071    0.06200  -1.141  0.25533   
## alpha   0.70397    0.24539   2.869  0.00454 **
## A       4.11814    1.28602   3.202  0.00158 **
## k     117.42612   36.69439   3.200  0.00159 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6701 on 210 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.915e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    210     94.284                            
## 2    209     93.476  1 0.8080  1.8066 0.18037  
## 3    209     94.049  0 0.0000                  
## 4    208     92.278  1 1.7708  3.9916 0.04703 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 480.8052
## 2    3a 480.9548
## 3    3b 482.2701
## 4    3c 480.1833
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.47770    0.76684  -1.927 0.055342 .  
## phi   -0.05736    0.05840  -0.982 0.327194    
## alpha  0.71711    0.23947   2.995 0.003082 ** 
## A      3.10993    0.97399   3.193 0.001627 ** 
## k     93.87721   24.16809   3.884 0.000138 ***
## s      2.29208    1.06106   2.160 0.031902 *  
## p      0.24090    0.10388   2.319 0.021367 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6661 on 208 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 9.772e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97258, p-value = 0.0003382
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.61766, p-value = 0.5368
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1103 row(s) containing missing values (geom_path).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

Model selection 1

## Error in nls(fg_1_MBg5, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_MBg5, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3_MBg5, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    193     155.63                           
## 2    192     155.56  1 0.065766  0.0812 0.7760
## 3    191     155.37  1 0.190025  0.2336 0.6294
##   model      AIC
## 1     1 637.9079
## 2     2 639.8251
## 3     3 641.5855
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge   0.3291     1.3677   0.241  0.81011   
## A    4.3422     1.3161   3.299  0.00115 **
## k   74.7556    23.5156   3.179  0.00172 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.898 on 193 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.347e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    193     155.63                            
## 2    192     150.74  1 4.8884  6.2265 0.01343 *
## 3    192     154.08  0 0.0000                  
## 4    191     148.95  1 5.1280  6.5756 0.01111 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 637.9079
## 2    1a 633.6526
## 3    1b 637.9485
## 4    1c 633.3142
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge  0.12475    1.23334   0.101  0.91954   
## A   3.91208    1.28052   3.055  0.00257 **
## k  81.11830   29.28454   2.770  0.00616 **
## p   0.20293    0.08487   2.391  0.01777 * 
## s   1.89369    0.81015   2.337  0.02045 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8831 on 191 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 9.985e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88968, p-value = 7.905e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.7167, p-value = 0.08603
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 18 rows containing missing values (geom_point).
## Warning: Removed 1120 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    112     71.868                              
## 2    111     71.835  1 0.0329  0.0508 0.822012   
## 3    110     65.492  1 6.3433 10.6543 0.001464 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 293.4221
## 2     2 295.3694
## 3     3 286.7378
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     2.661840   6.389187   0.417 0.677771    
## phi   -0.008471   0.052926  -0.160 0.873131    
## alpha  0.889450   0.236538   3.760 0.000274 ***
## A      2.988847   2.587754   1.155 0.250595    
## k     91.219286  34.580837   2.638 0.009552 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7716 on 110 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.156e-06
##   (9 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    110     65.492                           
## 2    109     65.475  1 0.017090  0.0285 0.8664
## 3    109     65.393  0 0.000000               
## 4    108     65.369  1 0.024334  0.0402 0.8415
##   model      AIC
## 1     3 286.7378
## 2    3a 288.7078
## 3    3b 288.5645
## 4    3c 290.5217
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     2.661840   6.389187   0.417 0.677771    
## phi   -0.008471   0.052926  -0.160 0.873131    
## alpha  0.889450   0.236538   3.760 0.000274 ***
## A      2.988847   2.587754   1.155 0.250595    
## k     91.219286  34.580837   2.638 0.009552 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7716 on 110 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.156e-06
##   (9 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94359, p-value = 0.0001075
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.94042, p-value = 0.347
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1241 row(s) containing missing values (geom_path).

plotting 2

411 - Everglades

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6746     5130.8                                 
## 2   6745     5123.3  1  7.5387  9.9251  0.001638 ** 
## 3   6744     5096.7  1 26.5898 35.1839 3.148e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24245.14
## 2     2 24237.22
## 3     3 24204.10
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.776053   0.292393   6.074 1.31e-09 ***
## phi    0.012473   0.004555   2.738  0.00619 ** 
## alpha  0.198383   0.032661   6.074 1.32e-09 ***
## A      2.934492   0.141794  20.695  < 2e-16 ***
## k     32.834100   1.760311  18.652  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8693 on 6744 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.433e-06
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1   6744     5096.7                             
## 2   6743     5092.4  1 4.2864  5.6758 0.01723 * 
## 3   6743     5072.1  0 0.0000                   
## 4   6742     5064.9  1 7.1661  9.5390 0.00202 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 24204.10
## 2    3a 24200.42
## 3    3b 24173.40
## 4    3c 24165.86
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.806386   0.293626   6.152 8.09e-10 ***
## phi    0.013398   0.004547   2.946 0.003226 ** 
## alpha  0.207639   0.032343   6.420 1.46e-10 ***
## A      2.515559   0.122971  20.457  < 2e-16 ***
## k     31.259924   1.582294  19.756  < 2e-16 ***
## p      0.102758   0.028519   3.603 0.000317 ***
## s      1.756709   0.145437  12.079  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8667 on 6742 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.607e-06
##   (23 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   8257      15147                              
## 2   8256      15146  1   0.569   0.310 0.5777    
## 3   8255      14972  1 174.514  96.223 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 39278.06
## 2     2 39279.75
## 3     3 39186.02
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.024860   0.169677   0.147    0.884    
## phi   -0.001611   0.006338  -0.254    0.799    
## alpha  0.567513   0.055614  10.205   <2e-16 ***
## A      4.792958   0.189195  25.333   <2e-16 ***
## k     27.673568   2.788436   9.924   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.347 on 8255 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.14e-06
##   (55 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   8255      14972                              
## 2   8254      14959  1 12.834  7.0815 0.007803 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 39186.02
## 2    3a 39180.94
## 3    3b 39162.63
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -5.793e-02  1.647e-01  -0.352  0.72499    
## phi    3.718e-04  6.334e-03   0.059  0.95320    
## alpha  5.704e-01  5.512e-02  10.348  < 2e-16 ***
## A      1.507e+01  1.449e+01   1.040  0.29826    
## k      2.660e+03  1.249e+04   0.213  0.83133    
## s      3.446e-01  1.061e-01   3.247  0.00117 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.345 on 8254 degrees of freedom
## 
## Number of iterations to convergence: 37 
## Achieved convergence tolerance: 9.544e-06
##   (55 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).
## Warning: Removed 982 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1    887     1241.7                               
## 2    886     1239.0  1  2.6605  1.9025 0.168150   
## 3    885     1227.3  1 11.7138  8.4466 0.003748 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3673.208
## 2     2 3673.298
## 3     3 3666.844
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.16033    1.66699   1.896  0.05831 .  
## phi   -0.03937    0.02342  -1.681  0.09303 .  
## alpha  0.48299    0.15887   3.040  0.00243 ** 
## A      2.31843    0.51056   4.541 6.38e-06 ***
## k     34.64800   10.82215   3.202  0.00142 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.178 on 885 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.275e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    885     1227.3                            
## 2    884     1219.4  1 7.9234   5.744 0.01675 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 3666.844
## 2    3a 3663.080
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)   
## ge       3.26837    1.70317   1.919  0.05531 . 
## phi     -0.04226    0.02310  -1.830  0.06764 . 
## alpha    0.48763    0.15523   3.141  0.00174 **
## A        6.95559   11.35961   0.612  0.54049   
## k      766.64790 1829.53396   0.419  0.67529   
## p        0.13739    0.20013   0.687  0.49257   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.174 on 884 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 4.526e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92881, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.9933, p-value = 0.04623
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).
## Warning: Removed 1175 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    989     1325.2                              
## 2    988     1318.4  1  6.859  5.1401 0.023594 * 
## 3    987     1304.2  1 14.172 10.7249 0.001094 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4081.795
## 2     2 4078.647
## 3     3 4069.926
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.39354    1.51339   1.582  0.11407    
## phi    0.04322    0.02493   1.734  0.08327 .  
## alpha  0.38064    0.11207   3.396  0.00071 ***
## A      2.69216    0.58992   4.564 5.66e-06 ***
## k     34.26888    7.12171   4.812 1.73e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 987 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.388e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M231,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    987     1304.2                                
## 2    986     1280.1  1 24.092  18.556 1.814e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4069.926
## 2    3a 4053.430
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.02553    1.34865   1.502 0.133445    
## phi     0.04358    0.02469   1.765 0.077859 .  
## alpha   0.38068    0.11015   3.456 0.000572 ***
## A       6.67972    3.72361   1.794 0.073138 .  
## k     382.54985  320.06757   1.195 0.232290    
## p       0.12995    0.05498   2.364 0.018290 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.139 on 986 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.165e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93047, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.9621, p-value = 7.428e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).
## Warning: Removed 1218 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   3147     8391.5                               
## 2   3146     8379.2  1  12.31   4.6215 0.03165 *  
## 3   3145     8043.3  1 335.88 131.3332 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16065.44
## 2     2 16062.81
## 3     3 15935.94
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.62506    0.25336  -6.414 1.63e-10 ***
## phi    -0.02677    0.01763  -1.519    0.129    
## alpha   0.90146    0.07141  12.623  < 2e-16 ***
## A      12.59456    1.10356  11.413  < 2e-16 ***
## k     140.66983   11.14462  12.622  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.599 on 3145 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.489e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3145     8043.3                                
## 2   3144     7980.9  1 62.352 24.5630 7.572e-07 ***
## 3   3144     7999.7  0  0.000                      
## 4   3143     7977.2  1 22.481  8.8574  0.002941 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 15935.94
## 2    3a 15913.43
## 3    3b 15920.82
## 4    3c 15913.95
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.64909    0.24829  -6.642 3.64e-11 ***
## phi    -0.02102    0.01739  -1.208    0.227    
## alpha   0.87403    0.07235  12.081  < 2e-16 ***
## A      14.31804    1.37821  10.389  < 2e-16 ***
## k     235.55628   35.16208   6.699 2.47e-11 ***
## p       0.07893    0.01326   5.952 2.95e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.593 on 3144 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 2.076e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92246, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.2462, p-value = 1.553e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 39 rows containing missing values (geom_point).
## Warning: Removed 126 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1682     3596.1                                 
## 2   1681     3473.9  1 122.210  59.136 2.488e-14 ***
## 3   1680     3414.1  1  59.845  29.448 6.580e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7923.648
## 2     2 7867.390
## 3     3 7840.110
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.36498    0.40262  -3.390 0.000714 ***
## phi     0.15870    0.01737   9.138  < 2e-16 ***
## alpha   0.60936    0.10510   5.798 8.01e-09 ***
## A      15.07115    1.83522   8.212 4.28e-16 ***
## k     193.82437   22.80452   8.499  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.426 on 1680 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.465e-06
##   (292 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1680     3414.1                                
## 2   1679     3389.7  1 24.329 12.0508 0.0005308 ***
## 3   1679     3400.0  0  0.000                      
## 4   1678     3389.2  1 10.783  5.3384 0.0209811 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 7840.110
## 2    3a 7830.059
## 3    3b 7835.148
## 4    3c 7831.796
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     -1.3845     0.3958  -3.498 0.000481 ***
## phi     0.1585     0.0173   9.164  < 2e-16 ***
## alpha   0.6013     0.1037   5.799 7.95e-09 ***
## A      17.7899     2.5541   6.965 4.69e-12 ***
## k     311.5811    63.2632   4.925 9.26e-07 ***
## p       0.0510     0.0121   4.213 2.65e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.421 on 1679 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 2.437e-06
##   (292 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89276, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.9088, p-value = 0.3635
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 155 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    363     164.19                                
## 2    362     160.67  1 3.5196  7.9299  0.005129 ** 
## 3    361     153.60  1 7.0705 16.6175 5.628e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 863.6187
## 2     2 857.6877
## 3     3 843.2163
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.92530    0.38473  -5.004 8.78e-07 ***
## phi     0.05259    0.02300   2.287   0.0228 *  
## alpha   0.54117    0.12017   4.503 9.04e-06 ***
## A       9.71675    1.87058   5.194 3.44e-07 ***
## k     154.77456   35.99823   4.300 2.21e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6523 on 361 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.859e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    361     153.60                          
## 2    360     153.03  1 0.56727  1.3345 0.2488
## 3    360     152.99  0 0.00000               
## 4    359     152.98  1 0.00281  0.0066 0.9353
##   model      AIC
## 1     3 843.2163
## 2    3a 843.8621
## 3    3b 843.7494
## 4    3c 845.7427
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.92530    0.38473  -5.004 8.78e-07 ***
## phi     0.05259    0.02300   2.287   0.0228 *  
## alpha   0.54117    0.12017   4.503 9.04e-06 ***
## A       9.71675    1.87058   5.194 3.44e-07 ***
## k     154.77456   35.99823   4.300 2.21e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6523 on 361 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.859e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96738, p-value = 2.677e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.086269, p-value = 0.9313
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1183 row(s) containing missing values (geom_path).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1732     1437.1                                
## 2   1731     1421.1  1 15.983  19.468 1.086e-05 ***
## 3   1730     1341.5  1 79.624 102.682 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4817.306
## 2     2 4799.901
## 3     3 4701.862
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.41422    0.65814  -0.629    0.529    
## phi    0.08563    0.01402   6.108 1.24e-09 ***
## alpha  0.63878    0.05373  11.888  < 2e-16 ***
## A      2.82061    0.46094   6.119 1.16e-09 ***
## k     50.75980    7.41012   6.850 1.02e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8806 on 1730 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.708e-06
##   (21 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   1730     1341.5                               
## 2   1729     1330.6  1 10.953  14.233 0.000167 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4701.862
## 2    3a 4689.639
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.25683    0.70343  -0.365  0.71508    
## phi     0.08625    0.01399   6.167 8.65e-10 ***
## alpha   0.64873    0.05285  12.274  < 2e-16 ***
## A       3.82689    0.81201   4.713 2.64e-06 ***
## k     157.40858   53.18059   2.960  0.00312 ** 
## p       0.12119    0.01966   6.164 8.83e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8772 on 1729 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.005e-06
##   (21 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84605, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.7997, p-value = 1.589e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).
## Warning: Removed 1091 row(s) containing missing values (geom_path).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   2513     2563.7                                
## 2   2512     2557.8  1   5.935   5.8285 0.01584 *  
## 3   2511     2377.9  1 179.816 189.8777 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8302.884
## 2     2 8299.053
## 3     3 8117.647
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.97107    0.39890  -2.434   0.0150 *  
## phi    0.03627    0.01641   2.210   0.0272 *  
## alpha  0.77759    0.04949  15.711  < 2e-16 ***
## A      5.67586    0.70573   8.043 1.34e-15 ***
## k     88.39813    9.20937   9.599  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9731 on 2511 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.494e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   2511     2377.9                              
## 2   2510     2346.3  1 31.618  33.824 6.8e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8117.647
## 2    3a 8085.969
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -1.017070   0.386092  -2.634  0.00848 ** 
## phi     0.034878   0.016277   2.143  0.03223 *  
## alpha   0.774202   0.049157  15.750  < 2e-16 ***
## A       8.090056   1.260163   6.420 1.63e-10 ***
## k     211.201214  41.853922   5.046 4.83e-07 ***
## p       0.064354   0.008343   7.713 1.75e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9668 on 2510 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.149e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90314, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.0848, p-value = 1.166e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (geom_point).
## Warning: Removed 1001 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1691     2038.0                              
## 2   1690     2036.0  1   1.971   1.636 0.2011    
## 3   1689     1822.5  1 213.484 197.843 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6585.713
## 2     2 6586.074
## 3     3 6400.433
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.354376   0.639816  -0.554    0.580    
## phi    0.004082   0.018687   0.218    0.827    
## alpha  0.859053   0.053716  15.993  < 2e-16 ***
## A      5.821094   0.913239   6.374 2.37e-10 ***
## k     61.118140   6.483580   9.427  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.039 on 1689 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.827e-06
##   (59 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_MBg5", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_MBg5", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   1689     1822.5                               
## 2   1688     1790.0  1 32.513   30.66 3.56e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6400.433
## 2    3a 6371.940
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + 
##     ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.385749   0.624568  -0.618    0.537    
## phi     0.006924   0.018559   0.373    0.709    
## alpha   0.849827   0.053006  16.033  < 2e-16 ***
## A       7.708509   1.306468   5.900 4.38e-09 ***
## k     146.625086  25.985212   5.643 1.96e-08 ***
## p       0.083952   0.011123   7.548 7.20e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.03 on 1688 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 5.607e-06
##   (59 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92394, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.5297, p-value = 3.208e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 29 rows containing missing values (geom_point).
## Warning: Removed 925 row(s) containing missing values (geom_path).

plotting 2

M334 - Black Hills Coniferous Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    355     329.22                                 
## 2    354     329.12  1  0.0988  0.1063    0.7446    
## 3    353     306.69  1 22.4347 25.8224 6.081e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1055.669
## 2     2 1057.562
## 3     3 1034.287
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.20360    1.67740  -0.121  0.90346    
## phi   -0.01703    0.03551  -0.480  0.63178    
## alpha  0.76864    0.13256   5.798 1.49e-08 ***
## A      2.63805    0.94448   2.793  0.00550 ** 
## k     37.35520   11.31477   3.301  0.00106 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9321 on 353 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.275e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    353     306.69                          
## 2    352     306.69  1 0.00219  0.0025 0.9600
## 3    352     306.61  0 0.00000               
## 4    351     306.14  1 0.46172  0.5294 0.4674
##   model      AIC
## 1     3 1034.287
## 2    3a 1036.284
## 3    3b 1036.188
## 4    3c 1037.649
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.20360    1.67740  -0.121  0.90346    
## phi   -0.01703    0.03551  -0.480  0.63178    
## alpha  0.76864    0.13256   5.798 1.49e-08 ***
## A      2.63805    0.94448   2.793  0.00550 ** 
## k     37.35520   11.31477   3.301  0.00106 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9321 on 353 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.275e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.82213, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.998, p-value = 0.04572
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 48 rows containing missing values (geom_point).
## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3c
212 Laurentian Mixed Forest 3c
221 Eastern Broadleaf Forest 3b
222 Midwest Broadleaf Forest 3b
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3c
232 Outer Coastal Plain Mixed Forest 3c
234 Lower Mississippi Riverine Forest 3b
242 Pacific Lowland Mixed Forest 3
251 Prairie Parkland (Temperate) 2
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert 3c
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 1c
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert 3
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3c
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3b
M223 Ozark Broadleaf Forest Meadow 3a
M231 Ouachita Mixed Forest 3a
M242 Cascade Mixed Forest 3a
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3a
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 3
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3a
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3a
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3a
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 6877 2876 0.6855202 0.0459563 0.2652800 1.1057603 0.0295554 0.0000282 0.0191503 0.0399605 0.1569893 0.0014243 0.0830081 0.2309704 3.224703 2.9515083 3.497898 35.50621 31.601054 39.41137
212 Laurentian Mixed Forest east 22715 9499 0.8911082 0.0265673 0.5716238 1.2105926 0.0286043 0.0000104 0.0222833 0.0349253 0.2827939 0.0006410 0.2331701 0.3324176 2.795505 2.6246072 2.966403 31.25839 29.409089 33.10769
221 Eastern Broadleaf Forest east 7333 3571 -1.0270072 0.0134183 -1.2540822 -0.7999321 0.0212515 0.0000280 0.0108748 0.0316281 0.5200947 0.0015779 0.4422254 0.5979639 9.403659 5.8716698 12.935648 124.28112 -49.365221 297.92747
222 Midwest Broadleaf Forest east 5845 2589 -0.2933344 0.0448758 -0.7086354 0.1219667 0.0236480 0.0000789 0.0062383 0.0410578 0.4241844 0.0022551 0.3310860 0.5172828 9.038465 5.6969092 12.380021 194.36309 -25.233038 413.95922
223 Central Interior Broadleaf Forest east 10010 3864 -0.7216688 0.0156206 -0.9666633 -0.4766742 -0.0113731 0.0000385 -0.0235379 0.0007917 0.4740221 0.0016575 0.3942158 0.5538285 6.220919 5.7712096 6.670628 61.99943 53.804238 70.19463
231 Southeastern Mixed Forest east 13517 6193 1.9169822 0.0475696 1.4894662 2.3444983 0.0115680 0.0000205 0.0026952 0.0204408 0.5780726 0.0004637 0.5358633 0.6202818 3.920043 3.6505071 4.189580 19.57951 17.036259 22.12275
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.2105558 0.0405679 0.8157541 1.6053574 0.0046124 0.0000232 -0.0048336 0.0140584 0.5526314 0.0004659 0.5103213 0.5949414 4.470390 4.1221024 4.818677 26.55541 23.374254 29.73656
234 Lower Mississippi Riverine Forest east 1388 778 2.3381420 2.1566506 -0.5428103 5.2190944 -0.0286401 0.0004699 -0.0711646 0.0138843 0.7163784 0.0070719 0.5514047 0.8813521 5.327577 1.1955121 9.459643 46.97352 -103.388769 197.33581
242 Pacific Lowland Mixed Forest pacific 83 83 -0.7594860 4.1175112 -4.8017902 3.2828183 0.0644850 0.0049100 -0.0751037 0.2040737 0.9125757 0.1202673 0.2217233 1.6034282 9.934156 -0.2217079 20.090019 31.51695 -1.272733 64.30664
251 Prairie Parkland (Temperate) east 2295 906 0.1296752 0.2374862 -0.8261137 1.0854642 0.0197742 0.0001904 -0.0072887 0.0468371 NA NA NA NA 3.624652 2.9252504 4.324054 24.44082 15.975461 32.90617
255 Prairie Parkland (Subtropical) east 717 319 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -1.4777002 0.5880419 -2.9894731 0.0340726 -0.0573586 0.0034111 -0.1724987 0.0577816 0.7171105 0.0573457 0.2450119 1.1892092 3.109929 1.1897688 5.030090 93.87721 46.231403 141.52301
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 0.1247516 1.5211347 -2.3079704 2.5574736 NA NA NA NA NA NA NA NA 3.912076 1.3862998 6.437853 81.11830 23.355661 138.88093
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 2.6618399 40.8217080 -10.0000287 15.3237085 -0.0084711 0.0028012 -0.1133582 0.0964160 0.8894499 0.0559504 0.4206862 1.3582136 2.988847 -2.1394744 8.117168 91.21929 22.688183 159.75039
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 1.8063858 0.0862164 1.2307855 2.3819861 0.0133984 0.0000207 0.0044841 0.0223127 0.2076393 0.0010461 0.1442368 0.2710418 2.515559 2.2744975 2.756621 31.25992 28.158128 34.36172
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 -0.0579321 0.0271163 -0.3807269 0.2648628 0.0003718 0.0000401 -0.0120447 0.0127883 0.5703604 0.0030380 0.4623153 0.6784055 15.069965 -13.3283468 43.468277 2660.06949 -21820.836460 27140.97544
M223 Ozark Broadleaf Forest Meadow east 896 349 3.2683749 2.9007893 -0.0743544 6.6111042 -0.0422559 0.0005334 -0.0875839 0.0030721 0.4876283 0.0240952 0.1829733 0.7922832 6.955594 -15.3393517 29.250540 766.64790 -2824.089055 4357.38485
M231 Ouachita Mixed Forest east 1006 495 2.0255255 1.8188546 -0.6210270 4.6720781 0.0435758 0.0006095 -0.0048706 0.0920222 0.3806779 0.0121335 0.1645183 0.5968375 6.679720 -0.6273893 13.986830 382.54985 -245.542048 1010.64175
M242 Cascade Mixed Forest pacific 3224 3207 -1.6490940 0.0616499 -2.1359287 -1.1622594 -0.0210194 0.0003026 -0.0551259 0.0130870 0.8740265 0.0052339 0.7321773 1.0158758 14.318035 11.6157475 17.020323 235.55628 166.613332 304.49923
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -1.3845420 0.1566866 -2.1609272 -0.6081568 0.1585085 0.0002992 0.1245845 0.1924325 0.6012556 0.0107500 0.3978953 0.8046159 17.789925 12.7803942 22.799456 311.58107 187.497956 435.66419
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -1.9252963 0.1480148 -2.6818838 -1.1687088 0.0525901 0.0005289 0.0073617 0.0978184 0.5411726 0.0144408 0.3048515 0.7774937 9.716752 6.0381397 13.395364 154.77456 83.981998 225.56713
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 -0.2568292 0.4948178 -1.6364981 1.1228397 0.0862507 0.0001956 0.0588190 0.1136824 0.6487265 0.0027936 0.5450605 0.7523925 3.826887 2.2342522 5.419522 157.40858 53.103535 261.71363
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -1.0170704 0.1490670 -1.7741617 -0.2599790 0.0348775 0.0002649 0.0029595 0.0667955 0.7742019 0.0024164 0.6778102 0.8705936 8.090056 5.6189900 10.561122 211.20121 129.129459 293.27297
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 -0.3857489 0.3900848 -1.6107574 0.8392596 0.0069239 0.0003444 -0.0294779 0.0433256 0.8498266 0.0028096 0.7458627 0.9537905 7.708509 5.1460408 10.270977 146.62509 95.658460 197.59171
M334 Black Hills Coniferous Forest interior west 459 181 -0.2035974 2.8136685 -3.5025504 3.0953556 -0.0170308 0.0012608 -0.0868632 0.0528016 0.7686404 0.0175730 0.5079271 1.0293536 2.638048 0.7805277 4.495567 37.35520 15.102366 59.60803
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 12 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 13 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.34627179            0.06956085     0.48261106      0.2099325
## 2       pacific -0.13558134            0.01870581    -0.09891795     -0.1722447
## 3          east  0.55939449            0.05610031     0.66935110      0.4494379
## 4 interior west -0.07754135            0.03662731    -0.00575182     -0.1493309

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.018602357           3.494004e-08    0.018602425
## 2       pacific  0.003873419           1.108463e-03    0.006046007
## 3          east  0.010293188           1.321777e-03    0.012883872
## 4 interior west  0.004435749           1.058486e-03    0.006510382
##   95 % CI, lower
## 1    0.018602288
## 2    0.001700831
## 3    0.007702505
## 4    0.002361117

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.48480805             1.790528e-07     0.48480840
## 2       pacific     0.06845431             5.172192e-03     0.07859180
## 3          east     0.32593507             8.307784e-03     0.34221832
## 4 interior west     0.09041867             3.435108e-03     0.09715149
##   95 % CI, lower
## 1     0.48480770
## 2     0.05831681
## 3     0.30965181
## 4     0.08368586

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   6.466352
## 2       pacific  14.932589
## 3          east   5.537695
## 4 interior west   6.077999

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US   261.2923
## 2       pacific   250.0609
## 3          east   280.9557
## 4 interior west   154.1969

Analaysis 2: \(G_{TI-NoIngrow}\)

211 - Northeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6822     4506.3                                
## 2   6821     4494.3  1  12.03  18.259 1.954e-05 ***
## 3   6820     4166.4  1 327.82 536.606 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 21450.25
## 2     2 21434.01
## 3     3 20919.09
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    3.657e-01  1.786e-01   2.048   0.0406 *  
## phi   2.097e-02  4.896e-03   4.282 1.88e-05 ***
## alpha 7.955e-01  3.171e-02  25.090  < 2e-16 ***
## A     4.951e+00  2.039e-01  24.279  < 2e-16 ***
## k     1.149e+02  5.450e+00  21.079  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7816 on 6820 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 6.819e-06
##   (52 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6820     4166.4                                
## 2   6819     4166.4  1 0.0202  0.0331 0.8556890    
## 3   6819     4163.6  0 0.0000                      
## 4   6818     4156.9  1 6.7849 11.1285 0.0008547 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 20919.09
## 2    3a 20921.06
## 3    3b 20916.52
## 4    3c 20907.39
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.381383   0.179370   2.126 0.033519 *  
## phi    0.020098   0.004874   4.124 3.77e-05 ***
## alpha  0.798296   0.031589  25.271  < 2e-16 ***
## A      3.890913   0.208976  18.619  < 2e-16 ***
## k     78.768988   5.103269  15.435  < 2e-16 ***
## p      0.051308   0.013823   3.712 0.000207 ***
## s      1.402154   0.096921  14.467  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7808 on 6818 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.09e-06
##   (52 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 22 rows containing missing values (geom_point).
## Warning: Removed 1038 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18911      11656                                 
## 2  18906      11560  5   95.88   31.36 < 2.2e-16 ***
## 3  18905      10222  1 1337.88 2474.27 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 47432.75
## 2     2 47270.53
## 3     3 44946.68
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.608e-01  1.272e-01    4.41 1.04e-05 ***
## phi   3.743e-02  2.784e-03   13.44  < 2e-16 ***
## alpha 1.068e+00  1.930e-02   55.34  < 2e-16 ***
## A     6.099e+00  2.100e-01   29.05  < 2e-16 ***
## k     2.132e+02  8.068e+00   26.42  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7353 on 18905 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.41e-06
##   (3805 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18905      10222                                 
## 2  18904      10193  1 29.3436  54.421 1.685e-13 ***
## 3  18904      10096  0  0.0000                      
## 4  18903      10089  1  6.8545  12.843 0.0003396 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 44946.68
## 2    3a 44894.32
## 3    3b 44712.94
## 4    3c 44702.09
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.622651   0.128755   4.836 1.34e-06 ***
## phi    0.036859   0.002759  13.357  < 2e-16 ***
## alpha  1.068645   0.018946  56.404  < 2e-16 ***
## A      3.304583   0.108381  30.490  < 2e-16 ***
## k     74.721418   2.756747  27.105  < 2e-16 ***
## p      0.007008   0.001980   3.540 0.000401 ***
## s      1.487757   0.037057  40.148  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7306 on 18903 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.34e-06
##   (3805 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1880 rows containing missing values (geom_point).
## Warning: Removed 1031 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7266     7882.2                                
## 2   7265     7861.6  1   20.6  19.041 1.297e-05 ***
## 3   7264     7409.1  1  452.5 443.638 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28950.11
## 2     2 28933.09
## 3     3 28504.17
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.042425   0.110097  -9.468  < 2e-16 ***
## phi    0.019581   0.005046   3.880 0.000105 ***
## alpha  0.820298   0.036323  22.583  < 2e-16 ***
## A      7.072648   0.270924  26.106  < 2e-16 ***
## k     90.061611   5.708525  15.777  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.01 on 7264 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 8.363e-06
##   (64 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   7264     7409.1                            
## 2   7263     7404.8  1 4.3213  4.2385 0.03955 *
## 3   7263     7396.5  0 0.0000                  
## 4   7262     7394.7  1 1.7401  1.7089 0.19117  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 28504.17
## 2    3a 28501.93
## 3    3b 28493.73
## 4    3c 28494.02
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.06362    0.10896  -9.762  < 2e-16 ***
## phi     0.01944    0.00504   3.857 0.000116 ***
## alpha   0.82014    0.03622  22.645  < 2e-16 ***
## A       9.90386    1.51624   6.532 6.93e-11 ***
## k     200.80804   77.54484   2.590 0.009629 ** 
## s       0.75435    0.06776  11.132  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.009 on 7263 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.112e-06
##   (64 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 29 rows containing missing values (geom_point).
## Warning: Removed 1036 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   4839     3647.5                               
## 2   4838     3644.1  1   3.44   4.5652 0.03268 *  
## 3   4837     3291.3  1 352.76 518.4278 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15860.31
## 2     2 15857.74
## 3     3 15366.75
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    8.246e-03  2.146e-01   0.038   0.9693    
## phi   1.574e-02  7.750e-03   2.030   0.0424 *  
## alpha 9.714e-01  3.840e-02  25.295   <2e-16 ***
## A     6.925e+00  3.611e-01  19.177   <2e-16 ***
## k     1.403e+02  8.614e+00  16.285   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8249 on 4837 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.078e-07
##   (1003 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_222,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Warning in anovalist.nls(object, ...): models with response
## '"G_MassBal_g5_MgHaYr"' removed because response differs from model 1
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   4837     3291.3                            
## 2   4836     3287.5  1 3.8198   5.619 0.01781 *
## 3   4836     3288.1  0 0.0000                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 15366.75
## 2    3a 15363.13
## 3    3b 15363.93
## 4    3c 19360.41
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.924e-03  2.140e-01   0.009   0.9928    
## phi   1.541e-02  7.740e-03   1.992   0.0465 *  
## alpha 9.708e-01  3.835e-02  25.313   <2e-16 ***
## A     7.304e+00  4.317e-01  16.919   <2e-16 ***
## k     1.591e+02  1.336e+01  11.909   <2e-16 ***
## p     1.160e-02  4.592e-03   2.525   0.0116 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8245 on 4836 degrees of freedom
## 
## Number of iterations to convergence: 3 
## Achieved convergence tolerance: 9.256e-06
##   (1003 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 530 rows containing missing values (geom_point).
## Warning: Removed 1053 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8742     7835.7                              
## 2   8741     7834.5  1   1.27   1.4168  0.234    
## 3   8740     7410.9  1 423.52 499.4683 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 31017.79
## 2     2 31018.38
## 3     3 30534.38
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.931980   0.107101  -8.702   <2e-16 ***
## phi    -0.007785   0.005843  -1.332    0.183    
## alpha   0.848540   0.035035  24.220   <2e-16 ***
## A      11.729351   0.676416  17.340   <2e-16 ***
## k     260.949648  19.492235  13.387   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9208 on 8740 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.652e-06
##   (1265 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8740     7410.9                                
## 2   8739     7365.7  1  45.22  53.651 2.607e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 30534.38
## 2    3a 30482.86
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.951410   0.105612  -9.009  < 2e-16 ***
## phi    -0.004955   0.005838  -0.849    0.396    
## alpha   0.849890   0.034520  24.620  < 2e-16 ***
## A      22.939833   3.801953   6.034 1.67e-09 ***
## k     732.507285 153.106819   4.784 1.74e-06 ***
## p       0.021022   0.002603   8.075 7.64e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9181 on 8739 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.744e-06
##   (1265 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 628 rows containing missing values (geom_point).
## Warning: Removed 1002 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  13233      26261                                  
## 2  13232      26221  1   39.73   20.047 7.621e-06 ***
## 3  13231      23383  1 2838.41 1606.090 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60936.50
## 2     2 60918.47
## 3     3 59404.05
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.365540   0.192401   7.097 1.34e-12 ***
## phi    0.016778   0.004675   3.589 0.000333 ***
## alpha  0.937866   0.020973  44.718  < 2e-16 ***
## A      5.253882   0.187488  28.023  < 2e-16 ***
## k     62.702798   2.803834  22.363  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.329 on 13231 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.3e-06
##   (281 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1  13231      23383                            
## 2  13230      23373  1 9.4160  5.3297 0.02098 *
## 3  13230      23348  0 0.0000                  
## 4  13229      23344  1 3.5243  1.9972 0.15761  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 59404.05
## 2    3a 59400.72
## 3    3b 59386.25
## 4    3c 59386.25
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.403917   0.194445   7.220 5.48e-13 ***
## phi    0.016848   0.004673   3.605 0.000313 ***
## alpha  0.939219   0.020886  44.968  < 2e-16 ***
## A      4.570986   0.187598  24.366  < 2e-16 ***
## k     46.752716   2.684293  17.417  < 2e-16 ***
## s      1.210934   0.047882  25.290  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.328 on 13230 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.779e-06
##   (281 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 139 rows containing missing values (geom_point).
## Warning: Removed 1017 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq   F value  Pr(>F)    
## 1  13303      28896                                
## 2  13302      28882  1   14.3    6.5638 0.01042 *  
## 3  13301      25616  1 3265.7 1695.7274 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 60049.81
## 2     2 60045.24
## 3     3 58450.62
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.016489   0.195833   5.191 2.13e-07 ***
## phi    0.006927   0.004944   1.401    0.161    
## alpha  0.962197   0.020564  46.790  < 2e-16 ***
## A      5.369908   0.204589  26.247  < 2e-16 ***
## k     68.553843   3.000312  22.849  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.388 on 13301 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.201e-07
##   (323 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  13301      25616                                 
## 2  13300      25615  1  0.5427  0.2818 0.5955465    
## 3  13300      25586  0  0.0000                      
## 4  13299      25562  1 24.2949 12.6398 0.0003789 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 58450.62
## 2    3a 58452.34
## 3    3b 58437.20
## 4    3c 58426.56
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.039161   0.196858   5.279 1.32e-07 ***
## phi    0.006382   0.004929   1.295 0.195421    
## alpha  0.964743   0.020399  47.295  < 2e-16 ***
## A      4.483501   0.191651  23.394  < 2e-16 ***
## k     49.948019   2.526469  19.770  < 2e-16 ***
## s      1.363086   0.070290  19.392  < 2e-16 ***
## p      0.028517   0.007624   3.740 0.000185 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.386 on 13299 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.867e-06
##   (323 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 178 rows containing missing values (geom_point).
## Warning: Removed 931 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1324     3905.3                              
## 2   1323     3904.4  1   0.883  0.2993 0.5844    
## 3   1322     3648.6  1 255.827 92.6948 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6664.563
## 2     2 6666.262
## 3     3 6578.334
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.20612    2.10603   1.522 0.128159    
## phi   -0.02311    0.02463  -0.938 0.348162    
## alpha  0.98799    0.09077  10.884  < 2e-16 ***
## A      3.64817    0.97321   3.749 0.000185 ***
## k     57.32926   10.48334   5.469 5.42e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.661 on 1322 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.039e-06
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1322     3648.6                          
## 2   1321     3648.2  1 0.33126  0.1199 0.7291
## 3   1321     3648.1  0 0.00000               
## 4   1320     3648.0  1 0.01897  0.0069 0.9340
##   model      AIC
## 1     3 6578.334
## 2    3a 6580.214
## 3    3b 6580.152
## 4    3c 6582.145
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.20612    2.10603   1.522 0.128159    
## phi   -0.02311    0.02463  -0.938 0.348162    
## alpha  0.98799    0.09077  10.884  < 2e-16 ***
## A      3.64817    0.97321   3.749 0.000185 ***
## k     57.32926   10.48334   5.469 5.42e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.661 on 1322 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 9.039e-06
##   (61 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84416, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.8168, p-value = 0.0001352
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 31 rows containing missing values (geom_point).
## Warning: Removed 645 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1     77     64.151                              
## 2     76     63.028  1 1.1223  1.3532 0.248350   
## 3     75     57.102  1 5.9260  7.7834 0.006682 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 340.6367
## 2     2 341.2248
## 3     3 335.3257
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge     0.42715    2.55649   0.167  0.86775   
## phi    0.08335    0.05221   1.596  0.11459   
## alpha  0.80394    0.26069   3.084  0.00286 **
## A      7.98885    4.05489   1.970  0.05251 . 
## k     99.77885   30.12593   3.312  0.00143 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8726 on 75 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.624e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1     75     57.102                          
## 2     74     57.042  1 0.06062  0.0786 0.7799
## 3     74     57.067  0 0.00000               
## 4     73     56.521  1 0.54607  0.7053 0.4038
##   model      AIC
## 1     3 335.3257
## 2    3a 337.2407
## 3    3b 337.2762
## 4    3c 338.5070
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge     0.42715    2.55649   0.167  0.86775   
## phi    0.08335    0.05221   1.596  0.11459   
## alpha  0.80394    0.26069   3.084  0.00286 **
## A      7.98885    4.05489   1.970  0.05251 . 
## k     99.77885   30.12593   3.312  0.00143 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8726 on 75 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.624e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98873, p-value = 0.7132
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.40173, p-value = 0.6879
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 725 row(s) containing missing values (geom_path).

plotting 2

251 - Prairie Parkland (Temperate)

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1785     1329.7                                 
## 2   1784     1327.5  1  2.1567  2.8983   0.08885 .  
## 3   1783     1304.4  1 23.1236 31.6086 2.185e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5834.037
## 2     2 5833.135
## 3     3 5803.715
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.43104    0.43342   0.995    0.320    
## phi    0.01366    0.01083   1.262    0.207    
## alpha  0.54040    0.09094   5.942 3.38e-09 ***
## A      4.69771    0.46209  10.166  < 2e-16 ***
## k     98.76330   12.00197   8.229 3.60e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8553 on 1783 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.537e-06
##   (507 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   1783     1304.4                              
## 2   1782     1298.5  1 5.8502  8.0283 0.004657 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 5803.715
## 2    3a 5797.678
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.41609    0.42989   0.968 0.333227    
## phi     0.01429    0.01081   1.322 0.186422    
## alpha   0.54611    0.08945   6.105 1.26e-09 ***
## A       5.80828    0.80793   7.189 9.56e-13 ***
## k     166.33129   37.05598   4.489 7.63e-06 ***
## p       0.04523    0.01165   3.883 0.000107 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8536 on 1782 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.558e-06
##   (507 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8823, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5432, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 276 rows containing missing values (geom_point).
## Warning: Removed 1176 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

Model selection 1

## Error in nls(fg_1_TI, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_TI, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3_TI, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    212     92.785                                
## 2    211     91.353  1 1.4322  3.3079 0.0703648 .  
## 3    210     86.638  1 4.7151 11.4287 0.0008622 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 433.8518
## 2     2 432.5074
## 3     3 423.1138
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.04984    1.02836  -1.021 0.308482    
## phi    -0.09961    0.07240  -1.376 0.170350    
## alpha   0.91617    0.23751   3.857 0.000152 ***
## A       3.95268    1.46620   2.696 0.007590 ** 
## k     182.38588   64.03964   2.848 0.004836 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6423 on 210 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.473e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    210     86.638                          
## 2    209     85.710  1 0.92793  2.2627 0.1340
## 3    209     86.161  0 0.00000               
## 4    208     85.124  1 1.03782  2.5359 0.1128
##   model      AIC
## 1     3 423.1138
## 2    3a 422.7987
## 3    3b 423.9281
## 4    3c 423.3227
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.97741    1.06842  -0.915   0.3613    
## phi    -0.10424    0.07273  -1.433   0.1533    
## alpha   0.95350    0.23557   4.048 7.29e-05 ***
## A       5.77406    3.58786   1.609   0.1091    
## k     408.50291  365.17982   1.119   0.2646    
## p       0.03980    0.01937   2.054   0.0412 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6404 on 209 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.348e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97692, p-value = 0.001345
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.23931, p-value = 0.8109
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1103 row(s) containing missing values (geom_path).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

Model selection 1

## Error in nls(fg_1_TI, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2_TI, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg_3_TI, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    193     138.02                              
## 2    192     138.02  1 0.0005  0.0007 0.978628   
## 3    191     132.19  1 5.8256  8.4173 0.004153 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 536.3344
## 2     2 538.3336
## 3     3 531.8809
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge    1.493e+00  2.246e+00   0.665  0.50693   
## phi   9.014e-03  3.170e-02   0.284  0.77646   
## alpha 8.009e-01  2.475e-01   3.236  0.00143 **
## A     4.271e+00  1.699e+00   2.514  0.01277 * 
## k     1.435e+02  4.872e+01   2.945  0.00363 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8319 on 191 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.079e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    191     132.19                          
## 2    190     132.10  1 0.08918  0.1283 0.7206
##   model      AIC
## 1     3 531.8809
## 2    3a 533.7487
## 3    3b 533.8776
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge    1.493e+00  2.246e+00   0.665  0.50693   
## phi   9.014e-03  3.170e-02   0.284  0.77646   
## alpha 8.009e-01  2.475e-01   3.236  0.00143 **
## A     4.271e+00  1.699e+00   2.514  0.01277 * 
## k     1.435e+02  4.872e+01   2.945  0.00363 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8319 on 191 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.079e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.81814, p-value = 2.241e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.666, p-value = 0.007676
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).
## Warning: Removed 1120 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    112     56.909                               
## 2    111     56.885  1 0.0238  0.0465   0.8297    
## 3    110     48.377  1 8.5083 19.3463 2.53e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 240.3323
## 2     2 242.2841
## 3     3 225.6526
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.938491   3.418876   0.275   0.7842    
## phi    -0.007771   0.048191  -0.161   0.8722    
## alpha   1.052768   0.205983   5.111 1.36e-06 ***
## A       5.298591   3.456696   1.533   0.1282    
## k     177.482892  72.147530   2.460   0.0155 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6632 on 110 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.688e-06
##   (9 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Warning in anovalist.nls(object, ...): models with response
## 'c("G_MassBal_g5_MgHaYr", "G_MassBal_g5_MgHaYr")' removed because response
## differs from model 1
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    110     48.377                          
## 2    109     48.250  1 0.12645  0.2857 0.5941
##   model      AIC
## 1     3 225.6526
## 2    3a 227.3516
## 3    3b 288.5645
## 4    3c 290.5217
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.938491   3.418876   0.275   0.7842    
## phi    -0.007771   0.048191  -0.161   0.8722    
## alpha   1.052768   0.205983   5.111 1.36e-06 ***
## A       5.298591   3.456696   1.533   0.1282    
## k     177.482892  72.147530   2.460   0.0155 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6632 on 110 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.688e-06
##   (9 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90966, p-value = 9.988e-07
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.0573, p-value = 0.2904
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).
## Warning: Removed 1241 row(s) containing missing values (geom_path).

plotting 2

411 - Everglades

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6746     4413.5                                
## 2   6745     4396.6  1  16.91  25.939 3.619e-07 ***
## 3   6744     4029.6  1 367.01 614.229 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 20675.75
## 2     2 20651.84
## 3     3 20065.56
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.398e+00  2.730e-01   5.118 3.17e-07 ***
## phi   1.707e-02  4.813e-03   3.547 0.000392 ***
## alpha 8.092e-01  2.984e-02  27.113  < 2e-16 ***
## A     3.587e+00  1.898e-01  18.895  < 2e-16 ***
## k     1.031e+02  5.295e+00  19.476  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.773 on 6744 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.587e-06
##   (23 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6744     4029.6                                 
## 2   6743     4015.1  1 14.4359  24.244 8.691e-07 ***
## 3   6743     3994.3  0  0.0000                      
## 4   6742     3992.1  1  2.1737   3.671   0.05541 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 20065.56
## 2    3a 20043.33
## 3    3b 20008.20
## 4    3c 20006.53
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.371218   0.268817   5.101 3.47e-07 ***
## phi    0.017624   0.004784   3.684 0.000232 ***
## alpha  0.820585   0.029405  27.906  < 2e-16 ***
## A      2.611927   0.142928  18.274  < 2e-16 ***
## k     58.852104   2.622506  22.441  < 2e-16 ***
## p      0.030506   0.015128   2.017 0.043785 *  
## s      1.594515   0.104476  15.262  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7695 on 6742 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.515e-06
##   (23 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 15 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8257      12696                              
## 2   8256      12696  1   0.00   0.0001 0.9936    
## 3   8255      12323  1 372.38 249.4426 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36024.31
## 2     2 36026.31
## 3     3 35782.41
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.785e-01  1.860e-01   1.497    0.134    
## phi   3.295e-03  6.313e-03   0.522    0.602    
## alpha 8.864e-01  5.290e-02  16.758   <2e-16 ***
## A     5.687e+00  2.856e-01  19.911   <2e-16 ***
## k     1.059e+02  7.985e+00  13.265   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.222 on 8255 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.076e-06
##   (55 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   8255      12323                            
## 2   8254      12319  1 4.6764  3.1334 0.07674 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 35782.41
## 2    3a 35781.28
## 3    3b 35770.98
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.287e-01  1.829e-01   1.250  0.21128    
## phi   4.256e-03  6.308e-03   0.675  0.49987    
## alpha 8.880e-01  5.268e-02  16.858  < 2e-16 ***
## A     1.054e+01  3.304e+00   3.189  0.00143 ** 
## k     4.748e+02  3.854e+02   1.232  0.21800    
## s     6.739e-01  8.137e-02   8.282  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.221 on 8254 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.827e-06
##   (55 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 22 rows containing missing values (geom_point).
## Warning: Removed 982 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     1168.5                                
## 2    886     1164.3  1  4.111  3.1279   0.07731 .  
## 3    885     1115.3  1 48.992 38.8737 6.992e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3366.802
## 2     2 3365.666
## 3     3 3329.407
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      5.43806    2.92939   1.856 0.063732 .  
## phi    -0.05992    0.02366  -2.532 0.011501 *  
## alpha   1.04581    0.15261   6.853 1.36e-11 ***
## A       2.48517    0.79903   3.110 0.001929 ** 
## k     124.72196   35.78148   3.486 0.000515 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.123 on 885 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.526e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    885     1115.3                          
## 2    884     1114.7  1 0.63251  0.5016  0.479
##   model      AIC
## 1     3 3329.407
## 2    3a 3330.902
## 3    3b 3330.305
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      5.43806    2.92939   1.856 0.063732 .  
## phi    -0.05992    0.02366  -2.532 0.011501 *  
## alpha   1.04581    0.15261   6.853 1.36e-11 ***
## A       2.48517    0.79903   3.110 0.001929 ** 
## k     124.72196   35.78148   3.486 0.000515 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.123 on 885 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.526e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95534, p-value = 8.236e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.6093, p-value = 0.1076
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1175 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    989     1289.9                                
## 2    988     1271.2  1 18.635  14.483 0.0001501 ***
## 3    987     1198.1  1 73.104  60.222  2.11e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3745.090
## 2     2 3732.654
## 3     3 3675.901
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.57887    1.72043   1.499 0.134202    
## phi     0.07341    0.02789   2.632 0.008620 ** 
## alpha   0.91659    0.10866   8.436  < 2e-16 ***
## A       3.49591    0.92350   3.786 0.000163 ***
## k     116.20283   25.01927   4.645 3.87e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.102 on 987 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.102e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M231,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    987     1198.1                         
## 2    986     1195.9  1 2.2462   1.852 0.1739
##   model      AIC
## 1     3 3675.901
## 2    3a 3676.040
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.57887    1.72043   1.499 0.134202    
## phi     0.07341    0.02789   2.632 0.008620 ** 
## alpha   0.91659    0.10866   8.436  < 2e-16 ***
## A       3.49591    0.92350   3.786 0.000163 ***
## k     116.20283   25.01927   4.645 3.87e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.102 on 987 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.102e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92797, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.009, p-value = 6.097e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1218 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3147     6340.4                                
## 2   3146     6316.1  1  24.27  12.089 0.0005141 ***
## 3   3145     5958.1  1 357.99 188.965 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14546.02
## 2     2 14535.94
## 3     3 14354.14
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.60996    0.23841  -6.753 1.72e-11 ***
## phi    -0.04531    0.01675  -2.705  0.00686 ** 
## alpha   1.00760    0.06593  15.283  < 2e-16 ***
## A      10.50226    0.85758  12.246  < 2e-16 ***
## k     137.61759    9.89727  13.905  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.376 on 3145 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 8.48e-06
##   (74 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1   3145     5958.1                               
## 2   3144     5954.3  1  3.7936  2.0031 0.157076   
## 3   3144     5958.1  0  0.0000                    
## 4   3143     5944.5  1 13.6556  7.2201 0.007247 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 14354.14
## 2    3a 14354.13
## 3    3b 14356.14
## 4    3c 14350.91
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.59542    0.24027  -6.640 3.68e-11 ***
## phi    -0.04897    0.01686  -2.905  0.00370 ** 
## alpha   1.01257    0.06566  15.420  < 2e-16 ***
## A       9.21407    0.84256  10.936  < 2e-16 ***
## k     121.11173   11.59186  10.448  < 2e-16 ***
## p       0.07108    0.02178   3.263  0.00111 ** 
## s       1.36655    0.15013   9.102  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.375 on 3143 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.462e-06
##   (74 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90152, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.1427, p-value = 3.432e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (geom_point).
## Warning: Removed 126 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1682     2218.6                                 
## 2   1681     2162.2  1  56.358  43.815 4.841e-11 ***
## 3   1680     2038.6  1 123.664 101.913 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6757.119
## 2     2 6715.763
## 3     3 6618.527
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.99702    0.41076  -2.427   0.0153 *  
## phi     0.12234    0.01595   7.671 2.88e-14 ***
## alpha   0.91665    0.08262  11.094  < 2e-16 ***
## A      12.24045    1.36971   8.936  < 2e-16 ***
## k     222.56853   21.81811  10.201  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.102 on 1680 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.477e-06
##   (292 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1680     2038.6                         
## 2   1679     2036.4  1 2.1419  1.7660 0.1841
## 3   1679     2038.3  0 0.0000               
## 4   1678     2035.4  1 2.8694  2.3656 0.1242
##   model      AIC
## 1     3 6618.527
## 2    3a 6618.756
## 3    3b 6620.293
## 4    3c 6619.919
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.99702    0.41076  -2.427   0.0153 *  
## phi     0.12234    0.01595   7.671 2.88e-14 ***
## alpha   0.91665    0.08262  11.094  < 2e-16 ***
## A      12.24045    1.36971   8.936  < 2e-16 ***
## k     222.56853   21.81811  10.201  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.102 on 1680 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.477e-06
##   (292 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90484, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.2897, p-value = 0.1972
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 154 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    363     161.29                                 
## 2    362     154.66  1  6.6256  15.508 9.857e-05 ***
## 3    361     136.40  1 18.2578  48.320 1.702e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 797.8815
## 2     2 784.5289
## 3     3 740.5521
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -2.21807    0.30914  -7.175 4.13e-12 ***
## phi     0.06447    0.02175   2.964 0.003239 ** 
## alpha   0.86627    0.10803   8.019 1.50e-14 ***
## A      14.24293    3.14943   4.522 8.31e-06 ***
## k     249.50043   66.37567   3.759 0.000199 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6147 on 361 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.692e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    361     136.40                          
## 2    360     136.02  1 0.38581  1.0211 0.3129
## 3    360     135.97  0 0.00000               
## 4    359     135.97  1 0.00077  0.0020 0.9640
##   model      AIC
## 1     3 740.5521
## 2    3a 741.5154
## 3    3b 741.3927
## 4    3c 743.3906
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -2.21807    0.30914  -7.175 4.13e-12 ***
## phi     0.06447    0.02175   2.964 0.003239 ** 
## alpha   0.86627    0.10803   8.019 1.50e-14 ***
## A      14.24293    3.14943   4.522 8.31e-06 ***
## k     249.50043   66.37567   3.759 0.000199 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6147 on 361 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.692e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97187, p-value = 1.564e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.64985, p-value = 0.5158
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1183 row(s) containing missing values (geom_path).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1732     1220.2                                
## 2   1731     1202.9  1  17.31  24.909 6.614e-07 ***
## 3   1730     1067.9  1 134.97 218.651 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4008.309
## 2     2 3985.520
## 3     3 3781.028
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.41907    1.35136   1.050    0.294    
## phi    0.10188    0.01355   7.519 8.83e-14 ***
## alpha  0.87931    0.04822  18.237  < 2e-16 ***
## A      2.17931    0.50497   4.316 1.68e-05 ***
## k     98.38321   14.42372   6.821 1.25e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7857 on 1730 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.642e-06
##   (21 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   1730     1067.9                              
## 2   1729     1061.8  1 6.1655   10.04 0.001558 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 3781.028
## 2    3a 3772.982
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.58563    1.42035   1.116 0.264420    
## phi     0.10254    0.01353   7.576 5.76e-14 ***
## alpha   0.87942    0.04786  18.374  < 2e-16 ***
## A       2.91230    0.79372   3.669 0.000251 ***
## k     212.37226   63.61103   3.339 0.000860 ***
## p       0.05697    0.01227   4.644 3.68e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7836 on 1729 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.548e-06
##   (21 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87532, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6361, p-value = 3.55e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 10 rows containing missing values (geom_point).
## Warning: Removed 1091 row(s) containing missing values (geom_path).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1   2513     1908.3                                  
## 2   2512     1901.0  1   7.358   9.7229  0.001841 ** 
## 3   2511     1600.9  1 300.117 470.7424 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7070.262
## 2     2 7062.542
## 3     3 6632.226
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.37717    0.27362  -5.033 5.17e-07 ***
## phi     0.03924    0.01414   2.775  0.00557 ** 
## alpha   1.01750    0.03982  25.554  < 2e-16 ***
## A       8.47074    0.91518   9.256  < 2e-16 ***
## k     173.17394   17.04337  10.161  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7985 on 2511 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.27e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", "_TI", sep = "")), data = G_M332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2511     1600.9                                
## 2   2510     1592.1  1 8.7362  13.773 0.0002108 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6632.226
## 2    3a 6620.458
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.38360    0.27184  -5.090 3.85e-07 ***
## phi     0.03923    0.01408   2.786  0.00538 ** 
## alpha   1.01443    0.03978  25.499  < 2e-16 ***
## A      10.12922    1.26771   7.990 2.03e-15 ***
## k     246.09225   34.42542   7.149 1.14e-12 ***
## p       0.01807    0.00410   4.407 1.09e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7964 on 2510 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.621e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90034, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.0757, p-value = 3.861e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 53 rows containing missing values (geom_point).
## Warning: Removed 1001 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   1691     1694.2                               
## 2   1690     1691.9  1   2.301   2.2987 0.1297    
## 3   1689     1407.5  1 284.422 341.3086 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5853.124
## 2     2 5852.822
## 3     3 5543.039
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.64658    0.91472   0.707    0.480    
## phi     0.01125    0.01758   0.640    0.522    
## alpha   1.04361    0.04870  21.429  < 2e-16 ***
## A       6.02771    1.11412   5.410 7.19e-08 ***
## k     138.31144   14.06122   9.836  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9129 on 1689 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.421e-06
##   (59 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", "_TI", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1   1689     1407.5                           
## 2   1688     1402.6  1 4.9064  5.9048 0.0152 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 5543.039
## 2    3a 5539.124
## 3    3b 5515.516
## 4    3c       NA
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    3.154e-01  7.995e-01   0.394    0.693    
## phi   1.275e-02  1.740e-02   0.733    0.464    
## alpha 1.034e+00  4.801e-02  21.538   <2e-16 ***
## A     2.931e+01  2.764e+01   1.061    0.289    
## k     3.616e+03  6.681e+03   0.541    0.588    
## s     6.529e-01  5.619e-02  11.620   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9052 on 1688 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 2.171e-06
##   (59 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91475, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.4552, p-value = 8.383e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 25 rows containing missing values (geom_point).
## Warning: Removed 925 row(s) containing missing values (geom_path).

plotting 2

M334 - Black Hills Coniferous Forest

Model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)    
## 1    355     278.17                                
## 2    354     278.09  1  0.0814  0.1036   0.7477    
## 3    353     253.34  1 24.7464 34.4810 9.94e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 925.8321
## 2     2 927.7273
## 3     3 896.3622
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.94186    2.52533   0.373 0.709400    
## phi   -0.02184    0.03552  -0.615 0.539023    
## alpha  0.85618    0.12668   6.759 5.77e-11 ***
## A      1.93987    0.83170   2.332 0.020241 *  
## k     44.09669   12.98016   3.397 0.000758 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8472 on 353 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.239e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

Model selection 2

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    353     253.34                          
## 2    352     253.33  1 0.01554  0.0216 0.8833
## 3    352     253.12  0 0.00000               
## 4    351     252.76  1 0.36271  0.5037 0.4784
##   model      AIC
## 1     3 896.3622
## 2    3a 898.3402
## 3    3b 898.0543
## 4    3c 899.5409
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.94186    2.52533   0.373 0.709400    
## phi   -0.02184    0.03552  -0.615 0.539023    
## alpha  0.85618    0.12668   6.759 5.77e-11 ***
## A      1.93987    0.83170   2.332 0.020241 *  
## k     44.09669   12.98016   3.397 0.000758 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8472 on 353 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.239e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9216, p-value = 9.819e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.2145, p-value = 0.02679
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (geom_point).
## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

Model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3c
212 Laurentian Mixed Forest 3c
221 Eastern Broadleaf Forest 3b
222 Midwest Broadleaf Forest 3a
223 Central Interior Broadleaf Forest 3a
231 Southeastern Mixed Forest 3b
232 Outer Coastal Plain Mixed Forest 3c
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest 3
251 Prairie Parkland (Temperate) 3a
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert 3a
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe 3
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert 3
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3c
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3b
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest 3c
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 3
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3a
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3a
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3b
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 6877 2876 0.3813827 NA 0.0297623 0.7330031 0.0200983 NA 0.0105442 0.0296524 0.7982961 NA 0.7363717 0.8602205 3.890913 3.4812550 4.300570 78.76899 68.76499 88.77299
212 Laurentian Mixed Forest east 22715 9499 0.6226514 0.0165777 0.3702810 0.8750219 0.0368591 0.0000076 0.0314504 0.0422679 1.0686454 0.0003590 1.0315092 1.1057816 3.304583 3.0921468 3.517020 74.72142 69.31795 80.12489
221 Eastern Broadleaf Forest east 7333 3571 -1.0636225 0.0118719 -1.2772127 -0.8500322 0.0194395 0.0000254 0.0095594 0.0293196 0.8201387 0.0013117 0.7491423 0.8911351 9.903863 6.9315957 12.876130 200.80804 48.79761 352.81847
222 Midwest Broadleaf Forest east 5845 2589 0.0019241 0.0457906 -0.4175882 0.4214365 0.0154152 0.0000599 0.0002421 0.0305883 0.9707974 0.0014709 0.8956105 1.0459843 7.304322 6.4579491 8.150694 159.07772 132.88939 185.26604
223 Central Interior Broadleaf Forest east 10010 3864 -0.9514096 0.0111539 -1.1584345 -0.7443848 -0.0049552 0.0000341 -0.0164000 0.0064896 0.8498902 0.0011916 0.7822233 0.9175572 22.939833 15.4871092 30.392556 732.50729 432.38187 1032.63270
231 Southeastern Mixed Forest east 13517 6193 1.4039174 0.0378089 1.0227772 1.7850576 0.0168481 0.0000218 0.0076874 0.0260088 0.9392190 0.0004362 0.8982788 0.9801591 4.570986 4.2032672 4.938706 46.75272 41.49112 52.01431
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.0391611 0.0387531 0.6532911 1.4250310 0.0063819 0.0000243 -0.0032796 0.0160433 0.9647431 0.0004161 0.9247591 1.0047271 4.483501 4.1078373 4.859164 49.94802 44.99578 54.90026
234 Lower Mississippi Riverine Forest east 1388 778 3.2061166 4.4353415 -0.9253992 7.3376325 -0.0231143 0.0006066 -0.0714309 0.0252022 0.9879888 0.0082396 0.8099150 1.1660625 3.648168 1.7389690 5.557367 57.32926 36.76345 77.89506
242 Pacific Lowland Mixed Forest pacific 83 83 0.4271518 6.5356559 -4.6656432 5.5199468 0.0833513 0.0027259 -0.0206557 0.1873584 0.8039405 0.0679568 0.2846288 1.3232522 7.988850 -0.0889087 16.066609 99.77885 39.76492 159.79277
251 Prairie Parkland (Temperate) east 2295 906 0.4160933 0.1848091 -0.4270567 1.2592434 0.0142934 0.0001169 -0.0069161 0.0355029 0.5461081 0.0080014 0.3706695 0.7215467 5.808278 4.2236860 7.392869 166.33129 93.65355 239.00904
255 Prairie Parkland (Subtropical) east 717 319 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -0.9774064 1.1415138 -3.0836607 1.1288480 -0.1042428 0.0052903 -0.2476296 0.0391441 0.9535040 0.0554955 0.4890964 1.4179116 5.774063 -1.2989738 12.847099 408.50291 -311.40509 1128.41090
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 1.4933011 5.0443138 -2.9367597 5.9233620 0.0090137 0.0010049 -0.0535143 0.0715416 0.8009468 0.0612462 0.3128025 1.2890910 4.270666 0.9195742 7.621757 143.47518 47.37152 239.57884
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 0.9384911 11.6887108 -5.8369180 7.7139002 -0.0077709 0.0023224 -0.1032745 0.0877326 1.0527678 0.0424292 0.6445570 1.4609785 5.298591 -1.5517690 12.148951 177.48289 34.50342 320.46236
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 1.3712176 0.0722628 0.8442505 1.8981848 0.0176236 0.0000229 0.0082447 0.0270025 0.8205855 0.0008647 0.7629415 0.8782294 2.611927 2.3317440 2.892110 58.85210 53.71116 63.99305
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 0.2286808 0.0334608 -0.1298940 0.5872557 0.0042564 0.0000398 -0.0081097 0.0166225 0.8879967 0.0027747 0.7847393 0.9912541 10.536414 4.0592871 17.013540 474.80027 -280.69077 1230.29130
M223 Ozark Broadleaf Forest Meadow east 896 349 5.4380574 8.5813470 -0.3113115 11.1874263 -0.0599231 0.0005599 -0.1063646 -0.0134816 1.0458094 0.0232894 0.7462925 1.3453263 2.485168 0.9169512 4.053385 124.72196 54.49551 194.94842
M231 Ouachita Mixed Forest east 1006 495 2.5788680 2.9598848 -0.7972560 5.9549920 0.0734092 0.0007779 0.0186773 0.1281411 0.9165879 0.0118060 0.7033660 1.1298098 3.495909 1.6836651 5.308152 116.20283 67.10575 165.29992
M242 Cascade Mixed Forest pacific 3224 3207 -1.5954198 0.0577315 -2.0665291 -1.1243105 -0.0489659 0.0002842 -0.0820186 -0.0159132 1.0125662 0.0043118 0.8838166 1.1413157 9.214068 7.5620528 10.866082 121.11173 98.38335 143.84011
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -0.9970190 0.1687257 -1.8026789 -0.1913590 0.1223354 0.0002544 0.0910544 0.1536164 0.9166482 0.0068265 0.7545941 1.0787024 12.240446 9.5539198 14.926973 222.56853 179.77498 265.36208
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.2180673 0.0955661 -2.8260042 -1.6101305 0.0644689 0.0004731 0.0216938 0.1072441 0.8662694 0.0116697 0.6538289 1.0787098 14.242926 8.0493969 20.436455 249.50043 118.96889 380.03197
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 1.5856303 2.0173850 -1.2001483 4.3714090 0.1025412 0.0001832 0.0759956 0.1290868 0.8794185 0.0022908 0.7855437 0.9732933 2.912305 1.3555472 4.469063 212.37226 87.60958 337.13493
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -1.3836032 0.0738987 -1.9166631 -0.8505433 0.0392317 0.0001983 0.0116182 0.0668452 1.0144294 0.0015827 0.9364181 1.0924406 10.129215 7.6433590 12.615071 246.09225 178.58712 313.59739
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 0.3153856 0.6391894 -1.2527167 1.8834879 0.0127471 0.0003027 -0.0213782 0.0468724 1.0340808 0.0023052 0.9399113 1.1282503 29.313158 -24.8961637 83.522479 3615.62183 -9487.31905 16718.56271
M334 Black Hills Coniferous Forest interior west 459 181 0.9418550 6.3772896 -4.0247284 5.9084385 -0.0218428 0.0012619 -0.0917063 0.0480207 0.8561804 0.0160479 0.6070374 1.1053234 1.939865 0.3041559 3.575575 44.09669 18.56853 69.62486
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 14 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 13 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.31871779            0.13688112     0.58700478      0.0504308
## 2       pacific -0.11882039            0.01971818    -0.08017276     -0.1574680
## 3          east  0.45163260            0.12330068     0.69330193      0.2099633
## 4 interior west -0.01409442            0.05607653     0.09581557     -0.1240044

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.018934720           5.460508e-08    0.018934827
## 2       pacific  0.001224769           1.087294e-03    0.003355866
## 3          east  0.012504457           2.788122e-03    0.017969176
## 4 interior west  0.005205494           1.024075e-03    0.007212682
##   95 % CI, lower
## 1   0.0189346130
## 2  -0.0009063281
## 3   0.0070397368
## 4   0.0031983065

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.91812588             2.996704e-07     0.91812647
## 2       pacific     0.08580768             4.631293e-03     0.09488502
## 3          east     0.71323424             1.640097e-02     0.74538014
## 4 interior west     0.11908395             3.297537e-03     0.12554712
##   95 % CI, lower
## 1     0.91812529
## 2     0.07673035
## 3     0.68108835
## 4     0.11262078

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   7.684198
## 2       pacific   9.905561
## 3          east   6.724078
## 4 interior west  11.765281

K (stand biomass at half biomss G in Mg/ha)

##          region weighted.k
## 1     entire US   278.5972
## 2       pacific   151.2149
## 3          east   173.5138
## 4 interior west   979.5360